Does Blender no longer support Make Human file format?
The MHX1 format is extremely old and has been deprecated (in favor of MHX2) for many years. MHX1 should not be used, and no modern version of MakeHuman supports it. 

Contrary to MHX1, MHX2 is an add-on that needs to be installed. It is not bundled with Blender. 

How to get MHX2 support is answered in a MakeHuman FAQ, see http://www.makehumancommunity.org/wiki/FAQ:What_happened_to_the_MHX_export_in_MH_1.1.x_and_later%3F

Quick summary:


In a Blender + MakeHuman 1.1.x setup, you need to install MHX2 from https://bitbucket.org/Diffeomorphic/mhx2-makehuman-exchange/overview
In a Blender + MakeHuman 1.2.x (currently in alpha) setup, both the MH side and Blender side of MHX2 are shipped with the MakeHuman zip.